Theorems · Theorem · functional analysis

ContinuousLinearMap.isTopCompl_range_ker_of_leftInverse

∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} {N : Type u_3} [inst_1 : TopologicalSpace M]
  [inst_2 : TopologicalSpace N] [inst_3 : AddCommGroup M] [inst_4 : AddCommGroup N] [inst_5 : Module R M]
  [inst_6 : Module R N] (f₁ : M →L[R] N) (f₂ : N →L[R] M),
  Function.LeftInverse ⇑f₂ ⇑f₁ → Submodule.IsTopCompl (↑f₁).range (↑f₂).ker

Defined in

Mathlib.Topology.Algebra.Module.Complement

Cited by

3 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingTopologicalSpaceTopologicalSpaceAddCommGroupAddCommGroupModuleModule